I am a mathematics student and am curious about how research in philosophy is done. In mathematics, let's say we have a geometric object, this object has various representations and each representation can make it easier to see some specific feature, for example: A geometric object could be the set of zeroes from a system of equations, it could be a set of distances from a certain set of points in a certain way, a category, etc.

In there, these are some kinds of most basic methods of research, each one revealing in a certain way. Are there such things in philosophical research? From my naive view until now, it seems that metaphysics, epistemology, ontology, dialetic, logic, etc are these most basic methods and they can be combined to yield additional insights. Is that correct?

I'm not sure if the tagging is adequate. If not, feel free to correct it.

I think your characterization of math research this way is off-base, and it sets the question up for nonsense. There are basic fields of math -- algebra, logic, analysis, geometry, combinatorics... And folks combine them via representation, algebraic topology, geometric combinatorial logic, ... But that is not characteristic of a general approach to math.
– jobermarkOct 8 '16 at 17:48

If you know this, then why be misleading? Too many people already depict math and various related sciences as this routine and mechanical process, compared to other disciplines. Proving anything important really is no more mechanical or straightforward than writing a novel. Why encourage them?
– jobermarkOct 9 '16 at 1:23

2 Answers
2

On the simplest level, my answer is no for most of your list (specifically, metaphysics, epistemology, ontology to which I might add ethics, social philosophy, every era in the history of philosophy). Instead, these are the things that people research rather than techniques used for doing research.

Dialectics is a hard one depending on what is meant by the term. By and large, contemporary philosophers will associate this with Hegel's philosophical method or with Marx's -- both of which are (largely though not universally) despised by the majority of philosophers.

Logic is for most philosophers a key part of their tool kit. Here, this should be taken to mean sentential logic, categorical logic, analogies, and (to differing degrees) modal logic. (For those who specifically study logic or philosophy of math as an area of research -- I believe we had one researcher who answered a few questions here for a bit -- the may also study more esoteric things like tri-valued logics or deontic logic which are not a part of the universal toolkit).

Having given the answer, no, I should explain several ways that this could prove to be an inadequate answer.

First, I'm working from my experience plus how I've seen other philosophers work. I can think of four types of philosophers I've encountered: contemporary analytics, contemporary continentals, historical figures or periods - translation / exposition, and historical figures or periods - comparative. For all categories, a major component of research is reading.

Maybe it might be easiest to start with the last two categories in terms of how the research process works. For historical translation / exposition philosophers, a good deal of what they do is read texts in the original language, provide translations, and argue about interpretations of the arguments. For historical comparative philosophers, they work with historical texts and contemporary texts to suggest either contemporary solutions to historical problems or historical solutions to contemporary problems (there's a good deal of variation where you could replace "solution" and "problem"). They key thing that makes this philosophy rather than history is that they are focused on offering arguments.

For contemporary analytics, most of their reading is going to be contemporary, and comparatively, they will have taken more logic. Also, some of them are going to need to be up to speed on research in other fields -- like neuroscience, chemistry, or psychology. The point is that they are offering arguments using logic and analogies to support positions on issues that matter to them.

Contemporary continentals sometimes do research like historical philosophers do. Others have what at least to me looks like a religious interest in some contemporary philosopher (for instance Judith Butler or Julia Kristeva or Martin Heidegger) where they mostly argue with others in their sub-discipline about interpretations or implementations.

All of that being said, people who write about ethics, social philosophy, aesthetics, or other similar things may often also include metaphysics/epistemology/etc as tools. As in they may give an account of art based on Kant's ideas in epistemology and art. Or they may give an account of morality building on Aristotle's account of human persons. The same pattern can also happen with epistemologists building on preferred metaphysics and then metaphysics people building on more fundamental metaphysics and logic. But it's also possible that they are positing something that is simultaneously metaphysics and epistemology rather than using any of these as a tool.

Others may have a different account of the sort of methods professional philosophers undertake... If so, I'll gladly defer to clearer accounts of how this works.

Maybe to make it more practical, here's what I do in my own research:

Type A

read a whole lot

notice something interesting in primary literature

focus in on secondary literature to see if I've got something interesting to say

compile the paper

revise and refine its arguments

submit, rinse, repeat

Type B

Have an insight that I think would make a good paper

Work on the argument / read papers in the vicinity of what I'm hoping to say

Either be convinced I have something worth saying and revise / add sources OR give up.

Further refinement

Submit, rinse, repeat

(Of course once it's accepted, there may still be a lot of work to do on it).

This takes months or even years in actual time (though actual time is interrupted by many other obligations).

If there's a better method that would get me either (a) better publications or (b) more publications for my time, I'd love to hear it.

Might I suggest this is not about philosophy, but about academia? You have separated the two before, in defense of the former against the oversights of the latter. But now you want to put them back together. I realize that Plato and Aristotle had live audiences, which is just the same thing in another form. But there are philosophers, e.g. Spinoza or Aquinas, whom I think did not have any of this in mind.
– jobermarkOct 10 '16 at 18:33

I took the question to be singularly focused on academic philosophy -- thus the comparison with math -- unless there's a type of non-academic math research.
– virmaiorOct 10 '16 at 22:33

No, but academic research in math is really the same, you either want something useful or you find something interesting, you rule out the idea someone else is going to get there before you and you just think, either alone or with others. Every non-experimental discipline is going to work the same way. That is about the structure of academia, not the nature of philosophy or math.
– jobermarkOct 10 '16 at 22:59

I would tend to agree, but I don't think that's quite true of every academic discipline. My experience in chemistry was that there are publishable papers to found by testing known hypotheses with already known techniques. But again, I took the question to be someone in academic math trying to grasp what are the methods / tools available for writing in academic philosophy and him/herself supplying a list that's broadly (but not always) wrong.
– virmaiorOct 10 '16 at 23:48

It is done in nearly the opposite way of mathematics. Mathematics typically starts with philosophical posits and then explores what they can find, whereas philosophy starts with the opposite: a question and sees if there is a reasonable answer.

The question leads the research. Write it down first, if you need to. And then keep track of references for what you explored.

If you end up merely aggregating information, you have informed yourself. If you end up having to synthesize what you have learned into new postulates to answer your question, you have created philosophy.